I'd start by finding the new models that fit your criteria. Then, search craigslist like a virus until you find one. ebay is also a good option.

What's kind of funny is that you described a BMX bike, but said you don't want a BMX. What about BMX don't you like? Not enough speed? If it's just the tires, you can change them.

Dahon makes sweet folding single speed bike. 20" wheels, but faster than a BMX and a lot more portable.